420 research outputs found
Synchronization in complex networks
Synchronization processes in populations of locally interacting elements are
in the focus of intense research in physical, biological, chemical,
technological and social systems. The many efforts devoted to understand
synchronization phenomena in natural systems take now advantage of the recent
theory of complex networks. In this review, we report the advances in the
comprehension of synchronization phenomena when oscillating elements are
constrained to interact in a complex network topology. We also overview the new
emergent features coming out from the interplay between the structure and the
function of the underlying pattern of connections. Extensive numerical work as
well as analytical approaches to the problem are presented. Finally, we review
several applications of synchronization in complex networks to different
disciplines: biological systems and neuroscience, engineering and computer
science, and economy and social sciences.Comment: Final version published in Physics Reports. More information
available at http://synchronets.googlepages.com
Network synchronization: Spectral versus statistical properties
We consider synchronization of weighted networks, possibly with asymmetrical
connections. We show that the synchronizability of the networks cannot be
directly inferred from their statistical properties. Small local changes in the
network structure can sensitively affect the eigenvalues relevant for
synchronization, while the gross statistical network properties remain
essentially unchanged. Consequently, commonly used statistical properties,
including the degree distribution, degree homogeneity, average degree, average
distance, degree correlation, and clustering coefficient, can fail to
characterize the synchronizability of networks
Delayed Dynamical Systems: Networks, Chimeras and Reservoir Computing
We present a systematic approach to reveal the correspondence between time
delay dynamics and networks of coupled oscillators. After early demonstrations
of the usefulness of spatio-temporal representations of time-delay system
dynamics, extensive research on optoelectronic feedback loops has revealed
their immense potential for realizing complex system dynamics such as chimeras
in rings of coupled oscillators and applications to reservoir computing.
Delayed dynamical systems have been enriched in recent years through the
application of digital signal processing techniques. Very recently, we have
showed that one can significantly extend the capabilities and implement
networks with arbitrary topologies through the use of field programmable gate
arrays (FPGAs). This architecture allows the design of appropriate filters and
multiple time delays which greatly extend the possibilities for exploring
synchronization patterns in arbitrary topological networks. This has enabled us
to explore complex dynamics on networks with nodes that can be perfectly
identical, introduce parameter heterogeneities and multiple time delays, as
well as change network topologies to control the formation and evolution of
patterns of synchrony
Experimental observation of chimera and cluster states in a minimal globally coupled network
A "chimera state" is a dynamical pattern that occurs in a network of coupled
identical oscillators when the symmetry of the oscillator population is broken
into synchronous and asynchronous parts. We report the experimental observation
of chimera and cluster states in a network of four globally coupled chaotic
opto-electronic oscillators. This is the minimal network that can support
chimera states, and our study provides new insight into the fundamental
mechanisms underlying their formation. We use a unified approach to determine
the stability of all the observed partially synchronous patterns, highlighting
the close relationship between chimera and cluster states as belonging to the
broader phenomenon of partial synchronization. Our approach is general in terms
of network size and connectivity. We also find that chimera states often appear
in regions of multistability between global, cluster, and desynchronized
states
- …